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Physica

Two exactly soluble models of a ferromagnet

Ger Vertogen, W.A. Smit

Published Mar 1, 1974• 3 citations
Publisher
DOI
10.1016/0031-8914(74)90213-4

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Physical review. B, Condensed matter•Mar 15, 1987•24 citations
A class of decorated spin 1/2 Ising models is introduced: all bonds of a hypercubic lattice parallel to one axis are decorated by n spins. Within each decorated bond, nearest neighbor ferromagnetic interactions compete with next-nearest neighbor antiferromagnetic interactions. An exact dedecoration transformation reduces the model to an anisotropic Ising model which is exactly soluble in two dimensions (d = 2) and for which accurate series expansion estimates are available for d = 3. Phase diagrams are presented for d = 2 and 3 : all exhibit a multiphase point at which many distinct, spatially modulated commensurate phases coexist. The variation of the characteristic wavevector and other properties are compared and contrasted with those of the axial next-nearest neighbor Ising (ANNNI) models.
An exact solution for a two-site crystal model, the smallest body-centered-cubic crystal, is presented for iron. The model consists of five d-like orbitals per site per spin, with interatomic hopping terms and an on-site Coulomb interaction of the fullest generality allowed by atomic symmetry. The ground state, depending on the choice of one-electron parameters, is found in one case to be a fully saturated ferromagnet, and in another to be an unsaturated ferromagnet with strong antiferromagnetic fluctuations. The many-body energy-level spectrum, intracluster charge and spin fluctuations, and photoemission and inverse photoemission densities of states for both cases are calculated and compared with experiment.